Description

Recall the definition of the Fibonacci numbers: 
f(1) = 1 
f(2)= 2 
f(n) = f(n-1) + f(n-2) (n >= 3) 

Given two numbers a and b, calculate how many Fibonacci numbers are in the range [a, b].

Input

The input contains several test cases. Each test case consists of two non-negative integer numbers a and b. Input is terminated by a = b = 0. Otherwise, a <= b <= 10^100. The numbers a and b are given with no superfluous leading zeros.

Output

For each test case output on a single line the number of Fibonacci numbers fi with a <= fi <= b.

Sample Input

10 100
1234567890 9876543210
0 0

Sample Output

5
4

HINT

Source

University of Ulm Local Contest 2000